Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 63

Answer

$\dfrac{4\sqrt{x}+8}{x-4}$

Work Step by Step

Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $ \dfrac{4}{\sqrt{x}-2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4}{\sqrt{x}-2}\cdot\dfrac{\sqrt{x}+2}{\sqrt{x}+2} \\\\= \dfrac{4\sqrt{x}+8}{(\sqrt{x})^2-(2)^2} \\\\= \dfrac{4\sqrt{x}+8}{x-4} .\end{array}
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